Combinatorial Multi-armed Bandits for Resource Allocation

Abstract

We study the sequential resource allocation problem where a decision maker repeatedly allocates budgets between resources. Motivating examples include allocating limited computing time or wireless spectrum bands to multiple users (i.e., resources). At each timestep, the decision maker should distribute its available budgets among different resources to maximize the expected reward, or equivalently to minimize the cumulative regret. In doing so, the decision maker should learn the value of the resources allocated for each user from feedback on each user s received reward. For example, users may send messages of different urgency over wireless spectrum bands; the reward generated by allocating spectrum to a user then depends on the message s urgency. We assume each user s reward follows a random process that is initially unknown. We design combinatorial multi-armed bandit algorithms to solve this problem with discrete or continuous budgets. We prove the proposed algorithms achieve logarithmic regrets under semi-bandit feedback.